PSCI 51087108 Advanced Data Analysis III

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PSCI 5108/7108Advanced Data Analysis III

• David Leblang
• leblang_at_colorado.edu

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Texts

• Texts from last semester
• Gujarati
• Kennedy
• Long and Freese (2003).
• Charemza and Deadman (1997).
• Enders (2004) -- optional

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What this course is about

• Models with limited dependent variables
• Models for time series data
• Models that pool cross-sections and time-series
• With limited dependent variables
• With continuous dependent variables

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Limited Dependent Variables

• Individual level behavior
• What factors determine which candidate an
  individual votes for?
• In a two-party system dependent variable is
  dichotomous ?use linear probability model, logit
  or probit
• In a multi-party system, dependent variable is
  polychotomouswith no specific ranking ? can use
  multinomial logit or conditional logit

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• Similar questions in comparative politics
• Which countries are democratic?
• Or in international politics
• What factors determine whether a country gets
  involved in a conflict?

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• Other questions concern the level/degree of
  intensity of a given response.
• Do you favor/oppose prayer in schools?
• Favor strongly
• Favor not strongly
• Oppose not strongly
• Oppose strongly
• Which opinion best describes your position?
• By law all students should pray in school
• By law no students should pray in school.
• These decisions should be left to the localities
• Ordered logit or ordered probit

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• Other related models we will cover
• Logit models for rare-events situations when
  the outcome occurs very infrequently (far less
  than 50 of the time).
• Probit models for simultaneous choices
  bivariate probit models with differing degrees of
  observability.

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Limited outcome models we will not cover (but can
if there is interest)

• Situations where the dependent variable is
  bounded
• What countries receive US foreign aid?
• Some countries receive zero
• Other countries receive lots.
• These are censored regression models (tobit
  models)
• Situations where the individual appears in the
  sample only if the value of their dependent
  variable is above a certain threshold (truncated
  regression models

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• Models were we only observe an outcome (e.g., a
  salary) if an earlier condition is met (e.g., the
  individual is employed).
• This is non-random selection ? individuals are
  assigned to the outcome/observation sample on the
  basis of some earlier model/decision.

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Other MLE Models (we will not cover)

• Models for event counts (poission, negative
  binomial models)
• Models for event histories (survival models

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Time Series Models

• (Taken from the Penn World Tables, v. 6.1
  http//pwt.econ.upenn.edu/)
• Country Year Pop Prices Cons. Gov't Inv.
• USA 1950 152594.16 100 95.1243 121.347
  106.393
• USA 1951 155605.88 100 94.2701 117.868
  106.421
• USA 1952 158617.61 100 94.2852 118.444
  104.006
• USA 1953 160625.43 100 94.3136 117.762
  104.493
• USA 1954 163637.16 100 94.4554 118.980
  104.958
• ...
• ...
• ...
• USA 2000 275423 100 100.478 128.568
  85.4658
• Note Population is in 1,000's C,I and G are in
  current U.S. dollars.
• GDP, Prices, Cons, etc. are each univariate time
  series.
• The critical feature of time series analysis is
  that observations have some logical order.
• Ideally, time series observations are
  equally-spaced. (E.g., one year apart, or one
  month apart.)

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Why we need special tools

• 1. Autocorrelation is common in time series data
  because the values of omitted
• causes are related from one period to the next.
• 2. Autocorrelation does not affect point
  estimates (i.e., it doesn't affect the estimates
  of the betas
• 3. It does affect the standard errors of the
  estimates.
• 4. GLS (or weighted least squares) can be used to
  correct the standard errors.
• Since it is only a re-weighting scheme, on
  average, it doesn't affect the point
• estimates.
• CRITICAL PROBLEM (2) above is based on the
  assumption that only
• the \no autocorrelation" assumption is violated.
  But if the omitted variables
• that cause the autocorrelation are also
  confounding variables, then
• E(Xet) 0 is violated also, introducing omitted
  variables bias. Generalized least squares does
  not fix this.

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Other issues

• Integrated and co-integrated series
• Simultaneous equations (VARs)
• Causality tests

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Pooled Cross-Section Time-Series Data

• Country Year Pop Prices Cons. Gov't Inv.
• CAN 1950 13753.32 81.976 80.034 94.007
  82.890
• CAN 1951 14149.10 87.562 85.165 97.855
  88.949
• CAN 1952 14544.88 94.751 92.189 107.266
  94.699
• ...
• ...
• ...
• ...
• ...
• ...
• ...
• CAN 2000 30750.00 79.2984 79.2705 109.141
  63.8771
• USA 1950 152594.16 100 95.1243 121.347
  106.393
• USA 1951 155605.88 100 94.2701 117.868
  106.421
• USA 1952 158617.61 100 94.2852 118.444
  104.006
• USA 1953 160625.43 100 94.3136 117.762
  104.493
• USA 1954 163637.16 100 94.4554 118.980
  104.958

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• When the number of time points is relatively
  small, this sort of data is sometimes referred to
  as panel data.
• Pooling data in this way introduces a level of
  complexity beyond that of standard time series
  analysis due to the heterogeneity of units.
• Don't confuse this sort of data with repeated
  cross-sections." The latter in-clude things like
  annual surveys in which different sets of
  respondents are interviewed each year.

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Fixes

• Fixed effects
• Random effects
• Different fixes depending on whether the panel is
  short and fat or tall and skinny

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Bigger problems when we combine cross-sectional
time-series data with limited outcome dependent
variables

• Conditional (fixed effects) logit and random
  effects probit
• bcsts models comparable to failure time data

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STATA

• Version 8
• Labs
• Student STATA